Question

all n x n matrices A such that the linear system Ax=0 has only the trivial solution
is this subspace

Answer 1

We are talking about a subspace of n x n matrices, a subset of all n x n matrices.

Answer 2

Also all such matrices are invertible and as such have a positive rank. There is no zero matrix (no zero vector).

Answer 3

so basically to show if this is closed under addition, we need to show that adding two invertible matrices gives you an invertible matrix.

Answer 4

Err as stated there is no zero vector, it already fails. Its not a subspace.

Answer 5

ah i see, nice :)